How to weld a vertex onto an edge
Add another edge loop in the crossbar piece (the top of the glasses) and move that edge loop near the vertices you are trying to join. So you'll something like this

|           |         |
*-----------*---------*
           *-*
           | |


Becomes this:

|          | |         |
*----------*-*---------*
           *-*
           | |


For more on adding loop cuts, click here

Then merge the vertices using Alt+M. 

Which becomes this:

|          | |         |
*----------*-*---------*
           | |


For more on merging : click here